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摘要: 针对一类在有限时间区间上重复作业的不确定非线性系统，本文提出一种重复学习控制方法，用于解决非参数不确定性问题.该方法采用死区修正学习律对期望控制输入与界函数进行估计，以避免参数的正向累加导致系统发散，并使该控制算法较少地依赖于系统信息，更方便于控制器的实现.基于Lyapunov方法所设计的控制器，保证了闭环系统所有信号的有界性，并使得跟踪误差收敛于死区界定的邻域.通过仿真算例及电机实验结果验证所提学习控制算法的有效性.
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关键词:
- 重复学习控制 /
- 非参数不确定性 /
- 死区修正 /
- Lyapunov方法
Abstract: This paper presents a repetitive learning control method to handle the nonparametric uncertain problem for a class of uncertain nonlinear systems performing a given repetitive task over a finite time interval. The learning laws with dead-zone modification are adopted to estimate the desired control input and bound functions, which avoids the divergency of estimates due to the ceaseless positive accumulation and facilitates the implementation of the controller with less knowledge about the system dynamics. The repetitive learning controller is designed in terms of Lyapunov synthesis, so as to guarantee the boundedness of all closed-loop signals while ensuring the tracking error to converge to the pre-specified neighbourhood. Numerical results for an inverted pendulum system and the AC motor experiment are conducted to testify the effectiveness of the proposed learning control scheme.1) 本文责任编委 王聪 -
图 10 界函数估计$\hat l_{f, \, k}$
Fig. 10 Estimate of the bound function $\hat l_{f, \, k}$
图 11 界函数估计$\hat l_{g, \, k}$
Fig. 11 Estimate of the bound function $\hat l_{g, \, k}$
图 12 误差性能指标$J_k$ (其中三条虚线为控制器(31)的实验结果, 实线为控制器(11)的实验结果
Fig. 12 Error performance index $J_k$ (the three dotted lines are the result by controller (31), the solid line is the result by controller (11))
图 13 控制输入$u_k$ (其中三条虚线为控制器(31)的实验结果, 实线为控制器(11)的实验结果)
Fig. 13 Control input $u_k$ (the three dotted lines are the result by controller (31), the solid line is the result by controller (11))
图 14 参考输入的估计$\hat u_k$ (其中三条虚线为控制器(31)的实验结果, 实线为控制器(11)的实验结果)
Fig. 14 Control input $\hat u_k$ (the three dotted lines are the result by controller (31), the solid line is the result by controller (11))
图 15 误差性能指标$J_k$ (其中三条虚线为控制器(31)的实验结果, 实线为控制器(11)的实验结果)
Fig. 15 Error performance index $J_k$ (the three dotted lines are the result by controller $ (31)$, the solid line is the result by controller $ (11)$)
图 16 控制输入$u_k$ (其中三条虚线为控制器(31)的实验结果, 实线为控制器(11)的实验结果)
Fig. 16 Control input $u_k$ (the three dotted lines are the result by controller (31), the solid line is the result by controller (11))
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